RE: How to Correct Measured Thrust for Density Altitude?
Hopefully I got the formula that he’s looking for… If you are confused try this simple step by step.
Thrust if a force and it’s also a product of mass flow rate and velocity of a moving gas from exhaust nozzle considering engine on a test stand. This formula can be derived from Newton's Law of Motion or Force = mass x acceleration. Acceleration (a) is a rate of change in velocity, at constant rate, a = (final minus initial velocity)/time, when started from rest initial velocity is zero. Therefore a = velocity/time. Subs to "a" in Force T = m * velocity/time. This can written as T = (mass/time) * velocity. Same thing when using change in momentum per unit time which is [(mass * velocity)final - (mass * velocity)initial]/time, initial velocity = 0
To make it short we can use Thrust Force T = (mass flow per unit time) * velocity
Mass = density * Volume, while Volume = Area * Distance of displacement,
Now using rate: mass flow rate = density * Volume flow rate
where Volume flow rate = Area * Distance/time, distance per unit time = velocity
Substitute those above expression to get Force (T)
T =density * Area * velocity * velocity
can be written simply as:
T = density * A * velocity ^2
This means that density has constant effect to Thrust while expo on velocity.
Using at least two data from test reading you may get T1 and T2 with functions as stated above, let's try another same maximum velocity where V2/V1 = 1, we can get
T2 = T1 *(density2/density1)
It can be used to determine new Thrust given with old Thrust T1, old and new density at same exhaust velocity.